Commercial Arithmetic 2 Questions and Answers - Form 3 Topical Mathematics

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Questions

  1. Chepkemoi bought a new washing machine for Kshs.420,000. Its value depreciated over
    the next 5years at the following rates; 15%, 13%, 12%, 9% and 7%. For the next 6 years,
    the rate of depreciation remained constant at 5% then the rate of depreciation remained at 4%
    each. How long did it take for the value of the washing machine to be
    1/3 of its original value?
  2. The table below shows income tax rates for the year 2006
    Taxable income in shs. Pa Rate of tax in %
    1 – 120,000 10
    120,001 – 240,000 15
    240,001 – 360,000 25
    360,001 – 480,000 35
    Over 480,000 50
    Nafula is married and claims a tax relief of shs.1,120 per month. She stays in a company house For which she pays a nominal rent of shs.1200 per month. She found that in a particular month, her employer deducted shs.4830 as tax. If she is entitled to a maximum insurance policy; relief of shs.600 per month. Calculate her monthly salary. (10mks)
  3. The figure below represents two pulley wheels, centres A and B with a rubber band CDEFGHC stretched round them.
    commercial arithmetic q3
    Radius of wheel centre A = 16cm, AB = 30cm. CD, 
    GF are tangents to the circles ∠ CAB = 86.3°
    1. calculate the length of the belt CD
    2. Find the angle ABD
    3. Find the length of the belt that would go round the pulleys (CDFGHC)
  4. In the figure below, ABCD is a cyclic quadrilateral and BD is a diagonal. EADF is a straight line, ∠CDF = 68o, ∠BDC = 45o and ∠BAE = 98o.
    commercial arithmetic q4
    Calculate the size of:
    1. ∠ABD.
    2. CBD
  5. A customer deposited Ksh.15,500 in a savings account. Find the accumulated amount after 3½ years if interest was paid at 16% per annum compounded semi-annually
  6. A retailer mixes three types of rice, Bismatti costing shs.120 per tin with Pishori costing shs.150 per tin and Ahero rice costing shs.80 per tin in the ratio x : 1 : 2 respectively. If he sells the mixture at shs.137.50 per tin making a profit of 25%. Calculate the value of x.
  7. Ashanti is a saleswoman and earns a commission on sales based on the monthly rates shown in the table below:- 
    Sales (Kshs) Commission rate % of sales
    The first 5000 10%
    The next 3000 15%
    Sales above 8000 20%
    In addition, she earns a basic monthly pay of Kshs.6700. During a certain month, she earned a total salary amounting to Kshs.8368. How much worth of sales did she make?
  8. The table below shows the annual income tax rates for a certain year.
     Total income per month in Kshs.   Rates in Kshs. Per £ 
     1-10164
    10165 – 19740
    19741 – 29316
    29317 – 33892
    388983 and above
     
     3 
     4 
     5
     6
     Automatic personal relief shs.1162 
    Kiptoo earns a monthly salary of Kshs.25000. He is entitled to house and medical allowances of Kshs.12000 and Kshs.3000 respectively
    Calculate:
    1. His taxable income per month
    2. His monthly tax payable
    3. His annual tax payable
  9. A company employee earns a basic salary of Kshs.25,000 and is also given taxable allowances amounting to Kshs.10,480. Using the table of taxation above:-
    1. Calculate the employee’s taxable income
    2. If the employee is entitled to a personal tax relief of Kshs.800 per month, determine the net tax
    3. If the employee was given 40% increase in his income, calculate the percentage increase in his income tax
  10. A certain amount of money was invested at compound interest of 10% compounded every two years for ten years. Given that the investor invested a total of 500,000/= at the end of the ten years, find the amount of money invested to the nearest shillings
  11. The cash price of a T.V set is Ksh. 26,000. Linda bought the set on hire purchase terms by paying a deposit of Ksh. 6,000 and the balance by 24 equal monthly installments of Kshs. 1,045.30. Find the compound rate interest per year.
  12. What would Kshs. 15000 amount to after 3 years at 16% per annum compounded quartely?
  13. Income rates for income earned were charged as follows:
     Income in Kshs. p.m.  Rate in Kshs per sh.20 
     1 - 8400
     8,401 - 18,000
     18,001 - 30,000
     30,001 - 36,000
     36,001 - 48,000
     48,001 and above 
     2
     3
     4
     5
     6
     7
    A civil servant earns a monthly salary of Ksh.19,200. His house allowance is Ksh12,000 per month. Other allowces per month are transport Ksh.1300 and medical allowance Ksh.2300.
    He is entitled to a family relief of Kshs. 1240 per month.
    Determine:
      1. His taxable income per month.
      2. Net tax.
    1. In addition, the following deductions were made
      NHIF                                      shs. 230
      Service charge                      Kshs. 100
      Loan repayment                    Kshs. 4000
      Co-operative shares of           Kshs. 1200
      Calculate his net salary per month
  14. Use the taxation rates in the table below to answer the questions that follow;-
    Taxable income in K £ p.a Rate % per K£
    1-4500
    4501-7500
    7501 – 10500
    10501 – 13500
    13501 – 16500
    0ver 16500
    10
    15
    20
    25
    30
    35
    The manager of a certain company is entitled to a monthly personal relief of shs.3000 and her tax (PAYE) is kshs.9000 per month she is also deducted NHIF shs.350 per month, WCPS shs.800 per month and cooperative shares shs.1200 per month, calculate
    1. The managers total deductions per month
    2. Total tax per month
    3. The manager’s annual gross salary
    4. The manager’s monthly basic salary if her monthly allowance and medical allowances are 10000 and 2000 shillings
  15. The table below shows the income tax for a certain year;
    Monthly taxable income (Kshs.) Tax rates (%)
    1- 9680
    9681- 18800
    18801 – 27920
    27921 – 37040
    37940 and above
    10%
    15%
    20%
    25%
    30%
    In that year, Odero paid a net tax of Kshs.5,512 per month. His total monthly taxable allowances amounted to Kshs.15,220 and he was entitled to a monthly personal relief of kshs.1,162. Every month the following deductions were made;
    N.H.I.F                             Kshs.320
    Union dues                       Kshs.200
    Co-operative shares          Kshs.7,500
    1. Calculate Odero’s monthly basic salary in Kshs
    2. Calculate his monthly salary
    1. A car is worth shs.800,000 when new. During the first year it depreciates by 20% of its value and in the second it deprecates by 5% of its value at the start of the year. During the third, fourth and fifth year, depreciation rate is 10%. How much less will it cost at the end of the fifth year?
    2. Find by how much the compound interest will exceed simple interest on shs.3,000 for two years at 15% per year
  16. The table below shows the income tax rates:

    Income per month (K
    £        Rate in Kshs per £
    1 - 325                                                2
    326 – 975                                            3
    976 - 1300                                           5
    1301 – 1625                                         6
    Over 1625                                            7.50
    Mr. Misoi is a public servant who lives in a government house and pays a nominal rent of Kshs.1,220 per month. He earns a basic salary of Kshs. 24,800 and a house allowance of Kshs.12,000 per month. He is entitled to a monthly relief of kshs.1620.
    1. Calculate his monthly;
      1. Taxable income in K£
      2. Tax payable without relief
      3. Tax after relief
    2. Apart from the income tax. The following monthly deductions are made from his earnings
      -HELB loan repayment Kshs.2400
      - Health insurance fund Kshs.1200
      - 2% of Basic salary union fee
      Calculate:-
      1. the total monthly deduction made on Mr. Misoi’s income
      2. Mr. Misoi’s net income per month
  17. Joseph bought a camera on hire purchase (H.P) term by paying a deposit of shs.7200 and cleared the balance in 24 equal monthly installments each of 1250.
    1. find the hire purchase price of the camera
    2. the hire purchase price of the camera is 24% higher than the cash price. Find the cash price of the camera
    3. Kangara took a loan from a financial institution and bought the camera with cash. He repaid the loan at 18% p.a compound interest at the end of the two years. Find the total interest paid by Kangara.
  18. Income tax for all the income earned was charged at the rates shown.
     Total Income p.a (K.£)  Rate in sh per K£
     1 – 1980
     1981 – 3960
    3961 – 6440
    6441 – 7920
    7921 – 9900
    Excess of 9900
     2 
     3 
     5 
     7 
     9
     10
    1. Wanyonyi earned a salary of Kshs.10,500 per month. In addition he was given a house allowance of Kshs. 6500 per month. He got tax relief of Kshs. 300 per month.
      Find ;
      1. His taxable income p.a
      2. Income tax he pays per month.
    2. A part from income tax the following deductions are made per month. NHIF of Kshs

Answers

  1. After 1st year = (95/100 x 4200000)
    = Shs.357,000
    After 2nd year = ( 87/100 x 357000)
    = sh310590
    After 3rd year = (88/100 x 310590
    = shs.273319.20
    After 4th year = ( 91/100 x 273319.20)
    =shs.248720.50
    After 5th year = (248720.50 x 93/100)
    The next 6 years = shs. 231310
    A = 231310 (1- 0.05)6 = 170034.10
    Then 140000 = 170034.10 (1-0.04)n
    (0.96)n = 140000/170034.10 = 0.8234
    n = log 0.8234/
    log 0.96
    = 0.0844/0.01773 = 4.76yrs
    Total no. of years = 5 + 6 + 4.76yrs = 15.76years
  2. Gross tax = 4830 + 1120 + 600 = sh 6550 per month
    Annual gross tax = 6550 X 12= 78,600
    10 X 120,000 = sh.12,000
    100
    15 X 120,000 = sh.18,000
    100
    25 X 120,000 = sh. 30,000
    100
    Re. tax = 78600 – (12000 + 18000+30000)
    =78600 – 60,000 = 18,6000
    35 X x =18,600
    100
    0.35x = 18,600
    x = sh 53142.86
    Taxable income p.a = 36,000+53142.86 =sh.412142.86
    Monthly salary = 413142.86/12 + 12,000
    = 34428.57 + 1200 = Sh 35628.57
  3.  
    1. Sin 86.3° = XB/AB
      Sin 86.3°= XB/30
      XB = 30sin86.3°
      XB = CD = 29.93746855 cm
    2. ∠ ABX = 90° - 86.3°
      = 3.7°
      ∴∠ ABD = 3.7° + 90°
      = 93.7°
    3. ∠ DBF obtuse = 360° - 187.4°
      = 172.6°
      Arc DEF = ø/360 πD or ø/360 x2πr
      But cos 86.3° = AX/AB
      Cos 86.3° = AX/30
      AX = 1.935969248 cm
      DB = 16 – 1.935969248 = 14.06403075 cm
      Arc DEF = 172.6°/360° 22 /7 x 14.06403075
      = 106807.8751
                2520
      = 42.38407742 cm
      Arc CGH
      reflex CAG = 360° - (2x 86.3°)
      = 187.4°
      ∴Arc CGH =187.4°/ 360° x2 x22 /7 x 16
      = 131,929.6
            2520
      = 52.35301587 cm
      Total length of belt to go round the belt
      = CD + DEF + GF + CHG
      = 29.93746855 + 42.38407742 + 29.93746855 + 52.35301587
      = 154.6120304 cm
      commercial arithmetic ans 3
  4. ABD = 310
    CBD = 370
  5.  A = 15,500(1 + 8/100)7
    = Ksh.25,707
  6.  
    commercial arithmetic answer 6
  7. Commission earned Kshs. (8368 – 6700) = Kshs. 1668/= 
    let sales in 3rd bracket be y
    10/100 x 5000) + (15/100 x 3000) + (20/100 x y) = 1668
    500 + 450 + 0.2y = 1668
    0.2y = 1668 – 950 = 718
    y =718/0.2 = 35%
    Total sales = (8000 + 3590)
    = shs.11590
  8.  
    1. Taxable income = (25000 + 12000 + 3000)= 40000
    2. Income tax
      10164 x 2/20 = Shs.1016.40
      10164 x 3/20 = Shs.1524.60
      10164 x 4/20 = Shs.2032.80
      Remaining :
      9508 x 5/20 = Shs.2377
      Total tax payable p.m = 6950.8 – 1162 = Shs.5788.80
    3. Annual tax payable = 5788.80 x 12 = Shs.69465.60
  9.  
    1. taxable income = Kshs. 25000 + Kshs.10480
      = Kshs. 35480
    2. tax charged:
      1st 4350 = 4350 x 2/20 = 683.25
      2nd 4555 = 4555 x 3/20 – 683.25
      3rd 4555 = 4555 x 4/20 – 911
      4th 4555 = 4555 x 5/20 - 1138.75
      Rem. 17465 = 17645 x 6/20 – 5239
      Total tax = 8407.5 - 800.00 = 7607.50
    3. 40/100 x 35480 – 14.192 = 49672
      New income = 35480 + 14192 = 49672
      Remainder = 49672 – 18015 = 31657
      Tax charged = 31657 x 6/20 =12665.1
      Total tax = 12665.1
      % increase in income ax = 4257.6 x 100
      7607.5 = 55.97%
  10. A = P(HR/100)n
    500000 = P( 1+ 20/100)5
    500,000 = (120/100)5
    500,000 = P
    (1.2)5
    P = Shs.200,938.786 ≈shs. 200,939
  11. Principal = 26, 000 - 6,000 = 20,000
    Total H.P instalments = 1045.3 x 24= 25087.20
    25087.20 = 20,000 [1/100 + r]2
    1.254 = [1+ r/100]2
    1.120 = 1/100 + r
    r/100 = 0.12 or 12%
  12. No. of periods =12
    r = 4% per period
    A = 1.0412 x 15000
    = 24015.5
  13.  
    1. Taxable income = 19200 + 12000 + 1300 + 2300 = 34800
    2. Net tax
      8400 x 2/20 = 840
      9600 x 3/20 = 1440
      12000 x 4/20 = 2400
      4800 x 5/20 = 1200/5800
      Net tax = 5800 – 1240
      = 4560
    3. Net salary = 34800 – (4560 + 5530)
      = 24710
  14.  
    1. 9000 + 350 + 800 + 1200 = 11350
    2. 9000 + 3000 = 12000
    3. Total taxes = 12000 x 12
      = shs.144000p.a
      Taxes
      450 x 2 = shs.9000
      3000 x 3 = shs.9000
      3000 x 4 = shs.12000
      3000 x 5 = shs.15000
      3000 x 6 = shs.18000
                       Shs.63,000
      144000 – 63000= shs.81000
      7y = 81000y = 11571
      Taxable income= 4500 + 3000 x 4 + 11571 = K 28071p.a
      Gross salary = shs. 561420p.a
    4. Total allowances = 12000 x 12
      = 144,000
      Basic salary = 561420 - 144000
      = Shs.417,420
      Monthly basic pay = shs. 34785
  15.  
    1. Net tax         5512
      Add relief      1162
      Tax payable   6674
      Tax on 9680 earned
      9680 X 10/100 = 968
      Tax on 9120 earned
      9120 x 15/100 = Shs. 1368
      Tax on next 9120 x 20/100 = Shs.1824
      Tax on next 9120 x 25/100 = 2280
      Total 968 + 1368 + 1824 + 2280 = 6440
      6674 – 6440 = 234
      Let x be charged at 30%
      30/100 X x = 234
      X = (234 X 100)/30 = Shs.780
      Total chargeable Income
      780 + (9120 x 3) + 9680 = 37820
      Salary 37820 – 15220 = Shs.2260 per month.
    2.  Net salary (37820 – 1270 – 6674) = Shs.29876
  16.  
    1. 1st year after dep. Of 20%
      800 000 x 80/100
      = Khs. 640,000……………………………………………………
      2nd year after dep. of 5%
      = 640000 x 95/100
      = 608,000 .....................................
      The next 3 yrs
      A = P [1 – R/100] = 608,000 ( 1 – 10/100)3
      = 698 000 (0.9)
      = Sh. 443,232 ……………………………………………………
      800,000 – 443,232 = Sh. 356,768 ………………………………………
    2. S.I = 3000 x 15/100 x 2
      = Sh 900 …………………………………………………
      A = 3000 [1 + 15/100]2
      = 3000[1.15]2
      = sh. 3967.50 ……………………………………………….
      C.I = sh 967.50
      967.50 – 900 = sh 67.50 ……………………………………….
  17.  
      1. Taxable Income
        [115/100 x 24 800[ + 12000 - 1220
        = 28520 + 12000 – 1220
        = Ksh.39,300
        = K₤ 1965 p.m.
      2. Tax due 325 x 2 = sh 650
        650 x 3 = sh 1950
        325 x 5 = sh 1725 ………………………..
        325 x 6 = sh 1950
        340 x 7.50 = sh 2250
        Total tax = sh. 8825 P.m………………………(without relief)
      1. Total deduction
        = sh (7280 + 2400 + 1200 + 2/100 of 24 800)……………….
        = (7280 + 2400 + 1200 + 496) + 1220
        = sh (11376 +_ 1220) = sh. 12,596 P.m …………………………………………
      2. Net income = sh (24800 + 1200 – 12596) = sh. 24,204 P.m……………………………
  18.  
    1. Total instalments = (24 x 1250)= Shs.30000
      H.P = 7200 + 30000= 37200
    2. 124% = 37200
      100% =
      C.P = 100/124 x 37200
      = 30000
    3. A = 30000 (1 + 18/100)2
      = 30000 (1.18)2 = 41772
      Total interest = 41772 – 30000 = 11772
  19.  
    1.  
      1. (10, 500 + 6,500) x 12 = K₤ 10,20 p.a
        20
      2. 1st 1980 x 2 =   Kshs. 3960
        2nd 1980 x 3 =  Kshs 5940
        3rd 2480 x 5 =  Kshs. 12 400
        4th 1480 x 7 =  Kshs. 10360
        5th 1980 x 9 =  Kshs.17 820
        Last 300 x 10 = Kshs 3 000
                                Kshs. 53 480
        PAYE = 53480/12 - 3000 x 12/100
        = Shs. 4156.70
      3. Net monthly pay
        17000 – 320 + 2/100 x 17000
        = 17000 – 660
        = Kshs 16 340.0

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